Product integration for Volterra integral equations of the second kind with weakly singular kernels

DOI10.1090/S0025-5718-96-00736-3zbMath0858.65136OpenAlexW2084148680MaRDI QIDQ4889927

Annamaria Palamara Orsi

Publication date: 25 March 1997

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-96-00736-3

zbMATH Keywords

convergencenumerical examplesproduct integrationweakly singular kernelsVolterra integral equations of the second kindNyström-type method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Singular nonlinear integral equations (45G05)

Related Items (45)

Error analysis of Jacobi–Galerkin method for solving weakly singular Volterra–Hammerstein integral equations ⋮ Numerical solution of weakly singular linear Volterra integro-differential equations ⋮ Solvability of quadratic integral equations with singular kernel ⋮ Piecewise-quasilinearization techniques for singularly perturbed Volterra integro-differential equations ⋮ A kind of product integration scheme for solving fractional ordinary differential equations ⋮ Product integration method for treating a nonlinear Volterra integral equation with a weakly singular kernel ⋮ Toeplitz matrix method and nonlinear integral equation of Hammerstein type ⋮ Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind ⋮ Numerical solution of the Fredholm singular integro-differential equation with Cauchy kernel by using Taylor-series expansion and Galerkin method ⋮ An effective method for approximating the solution of singular integral equations with Cauchy kernel type ⋮ An analytical and approximate solution for nonlinear Volterra partial integro-differential equations with a weakly singular kernel using the fractional differential transform method ⋮ Mechanical quadrature methods and their extrapolation for solving first kind Abel integral equations ⋮ Galerkin and multi-Galerkin methods for weakly singular Volterra-Hammerstein integral equations and their convergence analysis ⋮ Recursive higher order fuzzy transform method for numerical solution of Volterra integral equation with singular and nonsingular kernels ⋮ Singular asymptotic expansion and Legendre collocation method for two-term weakly singular Volterra integral equation of the second kind ⋮ On the numerical solution of Volterra integral equations on equispaced nodes ⋮ Fredholm-Volterra integral equation with singular kernel. ⋮ Note on numerical solution of the Fredholm singular integro-differential equation with Cauchy kernel by using Taylor-series expansion and Galerkin method ⋮ Singularity separation Chebyshev collocation method for weakly singular Volterra integral equations of the second kind ⋮ On solving a system of singular Volterra integral equations of convolution type ⋮ On the solution of quadratic nonlinear integral equation with different singular kernels ⋮ A new approach to the numerical solution of weakly singular Volterra integral equations. ⋮ A new numerical approximation for Volterra integral equations combining two quadrature rules ⋮ Numerical solution for system of singular nonlinear Volterra integro-differential equations by Newton-Product method ⋮ A Jacobi-collocation method for solving second kind Fredholm integral equations with weakly singular kernels ⋮ Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fredholm integral equations ⋮ Numerical solution of nonlinear weakly singular partial integro-differential equation via operational matrices ⋮ Fourth order scheme of exponential type for singularly perturbed volterra integro-differential equations ⋮ Numerical solution of two-dimensional weakly singular Volterra integral equations with non-smooth solutions ⋮ Smoothing transformation for numerical solution of nonlinear weakly singular Volterra integral equations using quasilinearization and product integration methods ⋮ Mathematical programming methods in the numerical solution of Volterra integral and integro-differential equations with weakly-singular kernel ⋮ Numerical solution of singular Volterra integral equations system of convolution type by using operational matrices ⋮ Difference schemes of exponential type for singularly perturbed Volterra integro-differential problems ⋮ Solving integral equations with logarithmic kernels by Chebyshev polynomials ⋮ Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions ⋮ On a method for solving a two-dimensional nonlinear integral equation of the second kind ⋮ A product integration approach based on new orthogonal polynomials for nonlinear weakly singular integral equations ⋮ Integro-differential equation with Cauchy kernel ⋮ A Nyström interpolant for some weakly singular linear Volterra integral equations ⋮ Legendre solutions of integral equations with logarithmic kernels ⋮ The Puiseux expansion and numerical integration to nonlinear weakly singular Volterra integral equations of the second kind ⋮ An adapted integration method for Volterra integral equation of the second kind with weakly singular kernel ⋮ Jacobi Spectral Methods for Volterra-Urysohn Integral Equations of Second Kind with Weakly Singular Kernels ⋮ Numerical solution of Fredholm-Volterra integral equation in one dimension with time dependence ⋮ Unnamed Item

Cites Work

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• A numerical approach to the solution of Abel integral equations of the second kind with nonsmooth solution
• Product integration methods for second-kind Abel integral equations
• On the order of the error in discretization methods for weakly singular second kind Volterra integral equations with non-smooth solutions
• Fast numerical solution of weakly singular Volterra integral equations
• Analysis of general quadrature methods for integral equations of the second kind
• Numerical solution of non-linear Volterra integral equations
• Runge-Kutta Theory for Volterra and Abel Integral Equations of the Second Kind
• Convergence Properties of a Class of Product Formulas for Weakly Singular Integral Equations
• Mean Convergence of Lagrange Interpolation. III
• Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
• Numerical Solution of Volterra Integral Equations with Continuous or Discontinuous Terms
• Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution
• Spline Function Approximations to the Solution of Singular Volterra Integral Equations of the Second Kind
• High Order Methods for a Class of Volterra Integral Equations with Weakly Singular Kernels
• An Existence Theorem for Abel Integral Equations
• Piecewise Polynomial Collocation for Volterra-type Integral Equations of the Second Kind
• Numerial Methods for Volterra Integral Equations with Singular Kernels
• Linear integral equations

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